A crucial chemical link between stars and their orbiting exoplanets is thought to exist. If universal, this connection could affect the formation and evolution of all planets. Therefore, this potential vital link needs testing by characterizing exoplanets around chemically-diverse stars. We present the discovery of two planets orbiting the metal-poor, kinematic thick-disc K-dwarf TOI-2345. TOI-2345 b is a super-Earth with a period of 1.05 d and TOI-2345 c is a sub-Neptune with a period of 21 d. In addition to the target being observed in four TESS sectors, we obtained five CHEOPS visits and 26 radial velocities from HARPS. By conducting a joint analysis of all the data, we find TOI-2345 b to have a radius of  R and a mass of  M⁠; and TOI-2345 c to have a radius of  R and a mass of  M⁠. To explore chemical links between these planets and their host star, we model their interior structures newly accounting for devolatized stellar abundances. TOI-2345 adds to the limited sample of well-characterized planetary systems around thick disc stars. This system challenges theories of formation and populations of planets around thick disc stars with its Ultra-Short Period super-Earth and the wide period distribution of these two planets spanning the radius valley.